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Author : A. I. Murdoch
Publisher : Cambridge University Press
Page : 439 pages
File Size : 45,8 Mb
Release : 2012-10-22
Category : Science
ISBN : 9780521765589
This authoritative reference book examines and clarifies physical assumptions implicit in continuum modelling from a molecular perspective.
Author : Leonid Ivanoviď Sedov
Publisher : Unknown
Page : 128 pages
File Size : 43,5 Mb
Release : 1972
Category : Continuum mechanics
ISBN : OCLC:873075136
Author : Leonid Ivanovich Sedov
Publisher : Unknown
Page : 242 pages
File Size : 41,7 Mb
Release : 1971
Category : Electronic
ISBN : 900179680X
Author : Stephen Bechtel,Robert Lowe
Publisher : Academic Press
Page : 340 pages
File Size : 50,7 Mb
Release : 2014-12-02
Category : Science
ISBN : 9780123948342
Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research
Author : Leonid I Sedov,Moscow State University Leonid I. Sedov (Institute of Mechanics, Russia)
Publisher : Unknown
Page : 100 pages
File Size : 44,9 Mb
Release : 1987-12-31
Category : Electronic
ISBN : 9028609245
Author : A. Ian Murdoch
Publisher : Cambridge University Press
Page : 128 pages
File Size : 54,7 Mb
Release : 2012-10-22
Category : Science
ISBN : 9781139788786
Ian Murdoch's Physical Foundations of Continuum Mechanics will interest engineers, mathematicians, and physicists who study the macroscopic behaviour of solids and fluids or engage in molecular dynamical simulations. In contrast to standard works on the subject, Murdoch's book examines physical assumptions implicit in continuum modelling from a molecular perspective. In so doing, physical interpretations of concepts and fields are clarified by emphasising both their microscopic origin and sensitivity to scales of length and time. Murdoch expertly applies this approach to theories of mixtures, generalised continua, fluid flow through porous media, and systems whose molecular content changes with time. Elements of statistical mechanics are included, for comparison, and two extensive appendices address relevant mathematical concepts and results. This unique and thorough work is an authoritative reference for both students and experts in the field.
Author : Kolumban Hutter,Klaus Jöhnk
Publisher : Springer Science & Business Media
Page : 645 pages
File Size : 51,9 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662064023
The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.
Author : C. S. Jog
Publisher : CRC Press
Page : 280 pages
File Size : 41,5 Mb
Release : 2002
Category : Continuum mechanics
ISBN : 0849324149
Author : John W. Rudnicki
Publisher : John Wiley & Sons
Page : 224 pages
File Size : 41,9 Mb
Release : 2014-09-22
Category : Science
ISBN : 9781118927670
A concise introductory course text on continuum mechanics Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics. A concise introductory course text on continuum mechanics Covers the fundamentals of continuum mechanics Uses modern tensor notation Contains problems and accompanied by a companion website hosting solutions Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering
Author : Attila Askar
Publisher : World Scientific
Page : 208 pages
File Size : 44,8 Mb
Release : 1986-07-01
Category : Electronic
ISBN : 9789814518956
This book presents a discussion of lattice dynamics for perfect and imperfect lattices and their relation to continuum theories of elasticity, piezoelectricity, viscoelasticity and plasticity. Some of the material is rather classical and close in spirit to solid state physics. A major aim here is to present a coherent theory for the four basic behavior types in the style of continuum mechanics. In each case, emphasis is on an explicit display of the physical mechanisms involved rather than general formalisms. The material is presented in terms of an atomistic picture for the discrete system. The basic ideas are believed to be relevant also at an intermediate scale in the continuum description of media with structure such as granular materials and composites.
Author : C. S. Jog
Publisher : Cambridge University Press
Page : 877 pages
File Size : 55,6 Mb
Release : 2015-06-25
Category : Science
ISBN : 9781107091351
"Presents several advanced topics including fourth-order tensors, differentiation of tensors, exponential and logarithmic tensors, and their application to nonlinear elasticity"--
Author : Karan S. Surana
Publisher : CRC Press
Page : 829 pages
File Size : 46,7 Mb
Release : 2022-01-24
Category : Science
ISBN : 9781000512342
This book provides physical and mathematical foundation as well as complete derivation of the mathematical descriptions and constitutive theories for deformation of solid and fluent continua, both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contra-variant bases. Definitions of co- and contra-variant tensors and tensor calculus are introduced using curvilinear frame and then specialized for Cartesian frame. Both Galilean and non-Galilean coordinate transformations are presented and used in establishing objective tensors and objective rates. Convected time derivatives are derived using the conventional approach as well as non-Galilean transformation and their significance is illustrated in finite deformation of solid continua as well as in the case of fluent continua. Constitutive theories are derived using entropy inequality and representation theorem. Decomposition of total deformation for solid and fluent continua into volumetric and distortional deformation is essential in providing a sound, general and rigorous framework for deriving constitutive theories. Energy methods and the principle of virtual work are demonstrated to be a small isolated subset of the calculus of variations. Differential form of the mathematical models and calculus of variations preclude energy methods and the principle of virtual work. The material in this book is developed from fundamental concepts at very basic level with gradual progression to advanced topics. This book contains core scientific knowledge associated with mathematical concepts and theories for deforming continuous matter to prepare graduate students for fundamental and basic research in engineering and sciences. The book presents detailed and consistent derivations with clarity and is ideal for self-study.
Author : Antonio Romano,Addolorata Marasco
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 49,9 Mb
Release : 2010-07-23
Category : Science
ISBN : 9780817648701
This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.
Author : W. Noll
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642658174
German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.
Author : Zishun Liu
Publisher : World Scientific
Page : 386 pages
File Size : 53,8 Mb
Release : 2024-02-06
Category : Technology & Engineering
ISBN : 9789811283802
This textbook offers a concise yet rigorous treatment of continuum mechanics at the introductory level. It differs from traditional textbooks by combining tensor analysis with mechanical analysis and teaching the former's basics within a single chapter. Readers of this book are not required to have learned tensor analysis in the context of engineering mathematics beforehand.The basic objectives of continuum mechanics are included in this textbook to facilitate an easy and thorough understanding of the concepts of continuum mechanics and elasticity. In addition, the mathematics and physics of deformation and kinematics are introduced and studied from the concept of stretch rather than from the traditional approach of strain. The large deformation problem of new smart soft materials is also introduced.This textbook provides illustrative examples and problem sets that enable readers to test their understanding of the subject matter and utilize the tools developed in the formulation of engineering problems. It is suitable for students whose undergraduate disciplines are non-mechanics-related fields. It also helps students or engineers who use the finite element method (FEM) to analyze problems to interpret the results produced by FEM software.